79 research outputs found
The Hilbert-Schmidt Theorem Formulation of the R-Matrix Theory
Using the Hilbert-Schmidt theorem, we reformulate the R-matrix theory in
terms of a uniformly and absolutely convergent expansion. Term by term
differentiation is possible with this expansion in the neighborhood of the
surface. Methods for improving the convergence are discussed when the
R-function series is truncated for practical applications.Comment: 16 pages, Late
Convergence of expansions in Schr\"odinger and Dirac eigenfunctions, with an application to the R-matrix theory
Expansion of a wave function in a basis of eigenfunctions of a differential
eigenvalue problem lies at the heart of the R-matrix methods for both the
Schr\"odinger and Dirac particles. A central issue that should be carefully
analyzed when functional series are applied is their convergence. In the
present paper, we study the properties of the eigenfunction expansions
appearing in nonrelativistic and relativistic -matrix theories. In
particular, we confirm the findings of Rosenthal [J. Phys. G: Nucl. Phys. 13,
491 (1987)] and Szmytkowski and Hinze [J. Phys. B: At. Mol. Opt. Phys. 29, 761
(1996); J. Phys. A: Math. Gen. 29, 6125 (1996)] that in the most popular
formulation of the R-matrix theory for Dirac particles, the functional series
fails to converge to a claimed limit.Comment: Revised version, accepted for publication in Journal of Mathematical
Physics, 21 pages, 1 figur
Relativistic coupled-cluster single-double calculations of positron-atom bound states
Relativistic coupled-cluster single-double approximation is used to calculate
positron-atom bound states. The method is tested on closed-shell atoms such as
Be, Mg, Ca, Zn, Cd, and Hg where a number of accurate calculations is
available. It is then used to calculate positron binding energies for a range
of open-shell transition metal atoms from Sc to Cu, from Y to Pd, and from Lu
to Pt. These systems possess Feshbach resonances, which can be used to search
for positron-atom binding experimentally through resonant annihilation or
scattering.Comment: submitted to Phys. Rev.
Elastic positron-cadmium scattering at low energies
The elastic and annihilation cross sections for positron-cadmium scattering are reported up to the positronium-formation threshold (at 2.2 eV). The low-energy phase shifts for the elastic scattering of positrons from cadmium were derived from the bound and pseudostate energies of a very large basis configuration-interaction calculation of the e+-Cd system. The s-wave binding energy is estimated to be 126±42 meV, with a scattering length of Ascat=(14.2±2.1)a0, while the threshold annihilation parameter, Zeff, was 93.9±26.5. The p-wave phase shift exhibits a weak shape resonance that results in a peak Zeff of 91±17 at a collision energy of about 490±50 meV
Calculation of the positron bound state with the copper atom
A new relativistic method for calculation of positron binding to atoms is
presented. The method combines a configuration interaction treatment of the
valence electron and the positron with a many-body perturbation theory
description of their interaction with the atomic core. We apply this method to
positron binding by the copper atom and obtain the binding energy of 170 meV (+
- 10%). To check the accuracy of the method we use a similar approach to
calculate the negative copper ion. The calculated electron affinity is 1.218
eV, in good agreement with the experimental value of 1.236 eV. The problem of
convergence of positron-atom bound state calculations is investigated, and
means to improve it are discussed. The relativistic character of the method and
its satisfactory convergence make it a suitable tool for heavier atoms.Comment: 15 pages, 5 figures, RevTe
Effective potentials for atom-atom interaction at low temperatures
We discuss the concept and design of effective atom-atom potentials that
accurately describe any physical processes involving only states around the
threshold. The existence of such potentials gives hope to a quantitative, and
systematic, understanding of quantum few-atom and quantum many-atom systems at
relatively low temperatures.Comment: 4 pages, 4 figure
The variable phase method used to calculate and correct scattering lengths
It is shown that the scattering length can be obtained by solving a Riccati
equation derived from variable phase theory. Two methods of solving it are
presented. The equation is used to predict how long-range interactions
influence the scattering length, and upper and lower bounds on the scattering
length are determined. The predictions are compared with others and it is shown
how they may be obtained from secular perturbation theory.Comment: 7 pages including 3 figure
Supersymmetry and the relationship between a class of singular potentials in arbitrary dimensions
The eigenvalues of the potentials
and
, and of the special cases of these potentials such as the Kratzer and
Goldman-Krivchenkov potentials, are obtained in N-dimensional space. The
explicit dependence of these potentials in higher-dimensional space is
discussed, which have not been previously covered.Comment: 13 pages article in LaTEX (uses standard article.sty). Please check
"http://www1.gantep.edu.tr/~ozer" for other studies of Nuclear Physics Group
at University of Gaziante
Theory and applications of atomic and ionic polarizabilities
Atomic polarization phenomena impinge upon a number of areas and processes in
physics. The dielectric constant and refractive index of any gas are examples
of macroscopic properties that are largely determined by the dipole
polarizability. When it comes to microscopic phenomena, the existence of
alkaline-earth anions and the recently discovered ability of positrons to bind
to many atoms are predominantly due to the polarization interaction. An
imperfect knowledge of atomic polarizabilities is presently looming as the
largest source of uncertainty in the new generation of optical frequency
standards. Accurate polarizabilities for the group I and II atoms and ions of
the periodic table have recently become available by a variety of techniques.
These include refined many-body perturbation theory and coupled-cluster
calculations sometimes combined with precise experimental data for selected
transitions, microwave spectroscopy of Rydberg atoms and ions, refractive index
measurements in microwave cavities, ab initio calculations of atomic structures
using explicitly correlated wave functions, interferometry with atom beams, and
velocity changes of laser cooled atoms induced by an electric field. This
review examines existing theoretical methods of determining atomic and ionic
polarizabilities, and discusses their relevance to various applications with
particular emphasis on cold-atom physics and the metrology of atomic frequency
standards.Comment: Review paper, 44 page
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